Perimeter

To solve the problem, we need to determine the perimeter of the shaded portion in the given figure. The shaded region consists of a semicircular arc and two straight line segments.

1. Understanding the Geometry:
The figure shows a semicircle with diameter . The points and are endpoints of the diameter, and is a point on the semicircle such that and . The shaded region includes the semicircular arc from to and the two straight line segments and .

2. Calculating the Diameter :
Since and are segments of the semicircle, the total length of the diameter is: Thus, the radius of the semicircle is:

3. Calculating the Length of the Semicircular Arc:
The circumference of a full circle is given by . For a semicircle, the arc length is half of the circumference: Given that , the arc length is:

4. Calculating the Perimeter of the Shaded Region:
The perimeter of the shaded region consists of the semicircular arc and the two straight line segments and . Therefore, the total perimeter is: Substituting the known values:

Final Answer:
The perimeter of the shaded portion is .